(a) If your life plan is to buy one lottery ticket every day for 5 days a week, 50 weeks a year for the next 50 years, where on any lottery ticket you have a one in 500,000,000 chance of winning the jackpot, what is the probability you will win the jackpot at least once in your lifetime? Hint: Let Wi be the event you win the jackpot with the ith lottery ticket. Assume these are independent. (b) (continued) Buying one such lottery ticket each day, how many lottery tickets would you need to buy to have a better than 10% chance of winning the jackpot at least once? Roughly how long will you need to live?